The Aruch Hashulchan299:16 quotes a dispute between all of the "heavy hitters" over the correct version of the g'mara in P'sachim 107. He quotes the opinion that when one recites havdala late (after dawn of Sunday morning), he only says borei p'ri hagafen and hamavdil ben kodesh l'chol (i.e. the non-whited-out parts here). And he only recites these b'rachosif he has not yet eaten. This appears to be the opinion of the Baha"g.

He quotes most others, including the Ram"a, who hold that one may still recite havdala until (and including) Tuesday even if one has eaten.

And to answer your first question, since the person is practically still waiting on Sunday to recite havdala, which is a mitzva, it should be treated like any other limited-time mitzva in that other activities (most prominent among which is eating) should not intervene.